A hybrid genetic fuzzy neural network algorithm designed for classification problems involving several groups

We propose a multigroup classification algorithm based on a hybrid genetic fuzzy neural net (GFNN) framework. Recent results on evolutionary computation and fuzzy neural network methodology are combined to effectively adapt the membership functions of the fuzzifier and the defuzzifier to the data set. Separate membership functions are defined for each dimension in the fuzzifier and for each fuzzy output group in the defuzzifier. The signal inherent in the fuzzifier is aggregated by a suitable T-norm and transmitted to the defuzzifier. The defuzzifier aggregates the response, i.e., the predicted group membership, by a suitable conorm. If misclassifications occur during training, the membership functions of both the fuzzifier and the defuzzifier are adapted by a systematic, robust procedure. The algorithm is successfully tested with real economic data. In total, the GFNN performs as good as the best of the competing methods in our test. The results suggest economically meaningful interpretations.

[1]  Jeffrey Horn,et al.  Multiobjective Optimization Using the Niched Pareto Genetic Algorithm , 1993 .

[2]  James J. Buckley,et al.  On the equivalence of neural nets and fuzzy expert systems , 1999 .

[3]  J. Buckley,et al.  Fuzzy input-output controllers are universal approximators , 1993 .

[4]  Hon Keung Kwan,et al.  A fuzzy neural network and its application to pattern recognition , 1994, IEEE Trans. Fuzzy Syst..

[5]  Hisao Ishibuchi,et al.  Efficient fuzzy partition of pattern space for classification problems , 1993 .

[6]  Zbigniew Michalewicz,et al.  Evolutionary Computation Techniques for Nonlinear Programming Problems , 1994 .

[7]  D. Sprecher.  On the structure of continuous functions of several variables , 1965 .

[8]  Hideo Tanaka,et al.  Construction of fuzzy classification systems with rectangular fuzzy rules using genetic algorithms , 1994, CVPR 1994.

[9]  Michio Sugeno,et al.  An Approach to Linguistic Instruction Based Learning , 1993, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[10]  Robert Fullér,et al.  Neural Fuzzy Systems , 1995 .

[11]  James C. Bezdek,et al.  Fuzzy Kohonen clustering networks , 1994, Pattern Recognit..

[12]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[13]  F. Glover,et al.  Simple but powerful goal programming models for discriminant problems , 1981 .

[14]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[15]  Hiroyuki Watanabe,et al.  Application of a fuzzy discrimination analysis for diagnosis of valvular heart disease , 1994, IEEE Trans. Fuzzy Syst..

[16]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[17]  V. Srinivasan,et al.  Multigroup Discriminant Analysis Using Linear Programming , 1997, Oper. Res..

[18]  Sankar K. Pal,et al.  Self-organizing neural network as a fuzzy classifier , 1994, IEEE Trans. Syst. Man Cybern..

[19]  Gunar E. Liepins,et al.  Some Guidelines for Genetic Algorithms with Penalty Functions , 1989, ICGA.

[20]  Ari Juels,et al.  Stochastic Hillclimbing as a Baseline Method for , 1994 .

[21]  H. Ishibuchi,et al.  Approximate Pattern Classification Using Neural Networks , 1993 .

[22]  Ralf Östermark,et al.  A fuzzy neural network algorithm for multigroup classification , 1999, Fuzzy Sets Syst..

[23]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[24]  Teuvo Kohonen,et al.  Self-organization and associative memory: 3rd edition , 1989 .

[25]  Zbigniew Michalewicz,et al.  Heuristic methods for evolutionary computation techniques , 1996, J. Heuristics.

[26]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[27]  Hahn-Ming Lee,et al.  A neural network architecture for classification of fuzzy inputs , 1994 .

[28]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[29]  Ralf Östermark,et al.  Addressing the multigroup discriminant problem using multivariate statistics and mathematical programming , 1998, Eur. J. Oper. Res..

[30]  Jack Sklansky,et al.  Constrained Genetic Optimization via Dynamic Reward-penalty Balancing and its Use in Pattern Recognition , 1993, Handbook of Pattern Recognition and Computer Vision.

[31]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..